Sparse Randomized Approximation of Normal Cycles

We develop a compression algorithm for the Normal-Cycles representations of shape, using the Nystrom approximation in Reproducing Kernel Hilbert Spaces and Ridge Leverage Score sampling. Our method has theoretical guarantees on the rate of convergence of the compression error, and the obtained approximations are shown to be useful for down-line tasks such as nonlinear shape registration in the Large Deformation Metric Mapping (LDDMM) framework, even for very high compression ratios. The performance of our algorithm is demonstrated on large-scale shape data from modern geometry processing datasets, and is shown to be fast and scalable with rapid error decay.